- Climate Submodel
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Purpose -
Climate is the driving mechanism for the model. Fundamental features of the desert
climate, including monthly temperature, surface temperature, precipitation, evapotranspiration,
and soil moisture are simulated.
- Approach -
To generate the needed variables, the model replicates some fundamental features
of the desert climate (i.e. mean temperature, mean maximum temperature, and precipitation).
Additionally, the model must simulate the extreme variability observed in these
measures within the desert climate using a "normal" statistical distribution.
Temperature data are further modified based on the topographical and elevation
changes across the landscape. Data from Landsat 5 were used in a statistical regression
to determine the appropriate dependence of temperature on solar azimuth angle
and elevation.
The soil water balance is calculated via the classic Thornthwaite method, developed
in 1948, with some modifications based on recent findings. Mean monthly temperature
values are used to calculate the potential evapotranspiration in each cell, and
the actual evapotranspiration depends on the degree of saturation of the soil.
The change in soil moisture in each month depends on the initial level of soil
moisture, the amount that evapotranspires, and the amount of water that infiltrates
the soil. Infiltration is assumed to be 100% during the gentle polar-front rains
of the winter, and 40% during the characteristically violent thunderstorms of
the Mojave summer. Soil moisture may vary between zero and a maximum given by
the available water content of the soil. Once this maximum is reached the soil
is saturated and all additional precipitation will leave the system as runoff.
- Temperature and precipitation generation-
A 20-year (1973-1992) historical temperature record from Barstow, California and
a 20-year precipitation record from the Goldstone Echo gauge on Fort Irwin were
used to simulate temperature and precipitation. Temperatures are not recorded
on Fort Irwin, but the NOAA station in Barstow, approximately 10 miles east of
Ft. Irwin, was a suitable data source.
Precipitation in any desert is extremely variable, though extremely low,
and this variability presents a modeling challenge. The precipitation-generation
module reproduces the variability of the precipitation yet maintains a reasonable
mean for the output.
As a general note, the one-month time step creates a disadvantage to the temperature-
and precipitation-generation techniques described above. No temporal autocorrelation
exists. In reality, a hot or wet July will probably be followed by a hot or wet
August. Currently, the model does not produce this behavior. As a result, the
simulated annual ranges in temperature and, particularly, in precipitation, are
not as great as the data suggest they should be. A potential solution to the absence
of temporal autocorrelation to tabulate the historical values of temperature and
precipitation and run them repetitively. We did not tabulate these values because
it removes the fundamental unpredictability of the desert climate. However, it
is certainly a valid alternative to the approach used here.
- Temperature modifications -
The lapse rate of temperature is the rate at which air temperature decreases as
altitude increases. Therefore, temperatures at any point should be adjusted by
the lapse rate.
Areas of land that receive more direct solar energy (insolation) will be warmer
than those that receive less. Topography and time of year determine the amount
of insolation received by a land area. Regions more perpendicular to the sun's
rays will receive more insolation, and therefore be warmer.
- The Water Balance
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The maximum amount of water that can be absorbed by the soil varies with
soil type, and is given by a quantity called Available Water Content (AWC).
An AWC value is the maximum possible soil moisture minus a typical, initial
value of soil moisture for that specific soil (Bedient and Huber, 1992).
Due to the high evapotranspiration and low precipitation rates, the typical
initial soil moisture was assumed to be equal to the minimum possible soil
moisture. AWC values for the nine dominant soils in Ft Irwin were obtained
from the U.S. Department of Agriculture, Soil Conservation Service located
in Davis, California. These data are given in units of "inches per
inch", meaning the available content in inches per inch of soil depth.
Since we wish to model the actual volume of water present in the soil, we
must assume a subsurface depth at which the existence of water will be unimportant
for plants; we call this depth the "depth of interest". We assume
a depth of interest of 30 centimeters, a reasonable approximation of the
typical "rooting" depth of plant species frequently consumed by
tortoises. This value, however, can be readily changed by adjusting the
Depth_of_interest converter in the STELLA model. There are five components
of the water balance model: precipitation (previously discussed), infiltration,
evapotranspiration, runoff, and change in soil moisture.
Infiltration:
General hydrologic principles related to recharge of aquifer systems indicate
that only 10% of precipitation will infiltrate the soil and find its way
to an aquifer system as recharge (Visocky, 1985). This is typical for recharge
in the midwest; however, this recharge is regulated and directed by the
large percentages of silts and clays associated with the soil matrix. Desert
soils do not contain high percentages of silts and clays and this allows
large amounts of precipitation to infiltrate under the right circumstances.
This is corroborated by the high permeabilities (rate of diffusion of a
fluid through a porous body under standard conditions of area, thickness
and pressure) found in desert soils. These permeabilities are as high as
20 inches of infiltration per hour for some soils. This allows us to assume
that all the precipitation that falls during the winter months infiltrates
into the soil because of the gentle nature and long period of this rainfall.
The short, intense nature of the summer rains motivates the assumption of
the lower infiltration rate of 40%, with 60% of the precipitation leaving
the system as runoff. Information collected and presented by Evans and Thames
(Evans, Sammis, and Cable, 1981) supports these general assumptions.
Evapotranspiration:
Evapotranspiration is the total of all water naturally leaving the ground
surface and the leaves of plants in gaseous form. Here we use the Thornthwaite
model of evapotranspiration (Thornthwaite, 1948), which is an empirically
derived relationship between mean monthly temperature and soil moisture.
The natural energy-demand for water is represented by Potential Evapotranspiration
(PET).
Actual evapotranspiration (AET) is that amount of moisture that leaves the
surface in gaseous form, and will differ from PET due to finite water availability.
Runoff:
In the Thornthwaite model, the water that neither infiltrates nor evaporates
is referred to as the surplus. Surplus water must either become surface
water at the cell where it falls or become "runoff", and flow
out of the cell; naturally, the terrain will determine which of these occurs.
We do not consider surface water here for a variety of reasons. Firstly,
in the current desert climate, though surface water may exist, it will generally
not stand for an entire month, which is the length of our time-step. Given
the terrain of Fort Irwin, semi-permanent surface water will be spatially
rare.
Since we explicitly assume no surface water, all surplus water in the water
balance must leave the system as runoff. We make an assumption that is very
important to note, namely that within each month, surplus water not only
leaves the cell on which it falls as precipitation, but that it leaves the
entire base. Runoff is constrained to be just the difference, if any, between
water that falls as precipitation and water that either infiltrates the
soil. The lesser value of Potential_infiltration and AWC minus C_Soil_Moisture
is the amount of water that infiltrates the soil.
Change in soil moisture:
The amount by which the stock of soil moisture changes is controlled by the
flow. If evapotranspiration exceeds infiltration, then there will always be
withdrawal from the stock. However, if more precipitation falls than can be
evaporated, the soil will be recharged only to the exten that it can absorb
water. If none of the above-mentioned constraints are encountered, the change
in soil moisture will be just the difference between the water that evapotranspires
from and the water that permeates into the soil.
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Available Water Content for Fort Irwin, California -
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